Admissibility criteria for nonuniform dichotomic behavior of nonautonomous systems on the whole line

摘要: Abstract We give new criteria for nonuniform dichotomy of nonautonomous systems on the whole line in terms admissibility relative to an integral equation. In our approach input space I ( R , X ) is intersection spaces that can be successively minimized and output C one some well-known continuous functions. Using computational arguments, we show leads a exponential dichotomy. expose complete analysis connections between also discuss several interesting consequences. Moreover, obtain explicit expression growth rates initial norm input-output operator. Finally, present direct application main result case evolution families which admit uniform growth.